There are two Diocese covering County Cork and parts of surrounding counties. The Church of Ireland is now known as "Cork, Cloyne and Ross". The Roman Catholic one is "Cork & Ross". The Roman Catholic Diocese of "Cloyne" has its Cathedral in Cobh, formerly Queenstown.
The town of Cloyne is situate in East County Cork and is between the town of Middleton and the Sea.
In relation to the marriage of John Hennessy and Elizabeth Sloane in 1841, I checked www.rootsireland.ie site and the Catholic list for the civil parish of Cloyne, but did not find any record.
However, a check on www.findmypast.ie has a record known as the Ffolliot Collection which has a a marriage recorded for June 6th 1841 of a John Hennessy and an Elizabeth Sloane at page 119.
I am of the opinion that this is the record you have found and I believe that this was a Church of Ireland Marriage and performed in the town of Cloyne. There are no addresses given, so you will need to make contact with the Representative Church Body, Churchtown, County Dublin to see if the Cloyne Church Records are available for 1841.